Fractionally Differenciate Data

Differenciates the time series data using the approximated binomial expression of the long-memory filter and an estimate of the memory parameter in the ARFIMA(p,d,q) model.

Usage

diffseries(x, d)

Arguments

x: numeric vector or univariate time series.
d: number specifiying the fractional difference order.

Value

the fractionally differenced series x.

Details

Since 2018, we are using (an important correction of) the fast algorithm based on the discrete Fourier transform (fft) by Jensen and Nielsen which is significantly faster for large n = length(x).

References

See those in fdSperio; additionally

Reisen, V. A. and Lopes, S. (1999) Some simulations and applications of forecasting long-memory time series models; Journal of Statistical Planning and Inference 80, 269–287.

Reisen, V. A. Cribari-Neto, F. and Jensen, M.J. (2003) Long Memory Inflationary Dynamics. The case of Brazil. Studies in Nonlinear Dynamics and Econometrics 7(3), 1–16.

Jensen, Andreas Noack and Nielsen, Morten Ørregaard (2014) A Fast Fractional Difference Algorithm. Journal of Time Series Analysis 35(5), 428–436; doi:10.1111/jtsa.12074 .

Author

Valderio A. Reisen valderio@cce.ufes.br and Artur J. Lemonte (first slow version), now hidden as diffseries.0().

Current version: Jensen and Nielsen (2014); tweaks by Martin Maechler, 2018.

Examples

memory.long <- fracdiff.sim(80, d = 0.3)
str(mGPH <- fdGPH(memory.long$series))
#> List of 3
#>  $ d     : num 0.135
#>  $ sd.as : num 0.347
#>  $ sd.reg: num 0.277
r <- diffseries(memory.long$series, d = mGPH$d)
#acf(r) # shouldn't show structure - ideally